Estimating Distinct Elements, Optimally. David Woodruff IBM Based on papers with Piotr Indyk, Daniel Kane, and Jelani Nelson. Problem Description. Given a long string of at most n distinct characters, count the number F 0 of distinct characters See characters one at a time
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Based on papers with Piotr Indyk, Daniel Kane, and Jelani Nelson
Combining upper and lower bounds, the complexity of this problem is:
Θ(ε-2+ log n) space and Θ(1) update and reporting time
Output (32R/K) * ln(1-T/K)/ln(1-1/K)
Ai, j = 1. Note if Ai,j = 1, then Ai’, j = 1 for all i’ < i
I = log R
The Ci are allowed to have bit representations of varying lengths len(Ci).
What is f(x,y)?
Combining upper and lower bounds, the streaming complexity of
estimating F0 up to a (1+ε) factor is:
Θ(ε-2+ log n) bits of space and Θ(1) update and reporting time